Sixtors and Mod 6 Computations

We consider the following phenomenon: with just one multiplication we can compute (3u+2v)(3x+2y)= 3ux+4vy mod 6, while computing the same polynomial modulo 5 needs 2 multiplications. We generalize this observation and we define some vectors, called sixtors, with remarkable zero-divisor properties. Using sixtors, we also generalize our earlier result (Computing ElementarySymmetric Polynomials with a Sub-Polynomial Number of Multiplications,ECCC Report TR02-052) for fast computation of much wider classes ofmulti-variate polynomials, modulo composites.